Statistical Reasoning for everyday life

Slides:

Advertisements

Similar presentations

Chapter 6 – Normal Probability Distributions

Advertisements

Sampling: Final and Initial Sample Size Determination

CHAPTER 8: Sampling Distributions

Chapter 7 Introduction to Sampling Distributions

Suppose we are interested in the digits in people’s phone numbers. There is some population mean (μ) and standard deviation (σ) Now suppose we take a sample.

Chapter Six Sampling Distributions McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 6-1 Introduction to Statistics Chapter 7 Sampling Distributions.

PROBABILITY AND SAMPLES: THE DISTRIBUTION OF SAMPLE MEANS.

6-5 The Central Limit Theorem

Population Proportion The fraction of values in a population which have a specific attribute p = Population proportion X = Number of items having the attribute.

Today Today: Chapter 8, start Chapter 9 Assignment: Recommended Questions: 9.1, 9.8, 9.20, 9.23, 9.25.

The Central Limit Theorem For simple random samples from any population with finite mean and variance, as n becomes increasingly large, the sampling distribution.

Sample Distribution Models for Means and Proportions

Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.

Continuous Probability Distribution  A continuous random variables (RV) has infinitely many possible outcomes  Probability is conveyed for a range of.

QUIZ CHAPTER Seven Psy302 Quantitative Methods. 1. A distribution of all sample means or sample variances that could be obtained in samples of a given.

Chapter 6 Sampling and Sampling Distributions

Section 8.1 ~ Sampling Distributions

AP Statistics Chapter 9 Notes.

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 8-1 Confidence Interval Estimation.

© 2003 Prentice-Hall, Inc.Chap 7-1 Basic Business Statistics (9 th Edition) Chapter 7 Sampling Distributions.

Chap 6-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition Chapter 6 Introduction to Sampling.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 6-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter.

Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 9 Samples.

Statistical Reasoning for everyday life Intro to Probability and Statistics Mr. Spering – Room 113.

McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 7 Sampling Distributions.

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.. Chap 7-1 Developing a Sampling Distribution Assume there is a population … Population size N=4.

Chapter 7 Sampling and Sampling Distributions ©. Simple Random Sample simple random sample Suppose that we want to select a sample of n objects from a.

Chap 7-1 Basic Business Statistics (10 th Edition) Chapter 7 Sampling Distributions.

Sampling Error SAMPLING ERROR-SINGLE MEAN The difference between a value (a statistic) computed from a sample and the corresponding value (a parameter)

Chapter 18: Sampling Distribution Models

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

Chapter 5 Sampling Distributions. The Concept of Sampling Distributions Parameter – numerical descriptive measure of a population. It is usually unknown.

Copyright © 2009 Pearson Education, Inc. 8.1 Sampling Distributions LEARNING GOAL Understand the fundamental ideas of sampling distributions and how the.

Sampling Theory and Some Important Sampling Distributions.

1 Pertemuan 14 Peubah Acak Normal Matakuliah: I0134-Metode Statistika Tahun: 2007.

Lecture 5 Introduction to Sampling Distributions.

Chapter 8 Interval Estimates For Proportions, Mean Differences And Proportion Differences.

MATH Section 4.4.

Copyright © 2014 Pearson Education. All rights reserved Sampling Distributions LEARNING GOAL Understand the fundamental ideas of sampling distributions.

Chapter 9 Day 2. Warm-up  If students picked numbers completely at random from the numbers 1 to 20, the proportion of times that the number 7 would be.

Sampling and Sampling Distributions

Sampling Distributions – Sample Means & Sample Proportions

Topic 8: Sampling Distributions

Chapter 7 Review.

Sampling Distributions

Chapter 6 Inferences Based on a Single Sample: Estimation with Confidence Intervals Slides for Optional Sections Section 7.5 Finite Population Correction.

Central Limit Theorem Sampling Distributions Central Limit Theorem

Chapter 7 Sampling and Sampling Distributions

Introduction to Sampling Distributions

Sec. 7-5: Central Limit Theorem

8.1 Sampling Distributions

8.1 Sampling Distributions

Chapter 7 Sampling Distributions.

Chapter 18: Sampling Distribution Models

Warm Up 1) A 2016 study from the State Department found that 46% of American citizens hold a passport. If repeated samples of 40 American citizens are.

Central Limit Theorem General version.

Chapter 7 Sampling Distributions.

Sampling Distributions

Population Proportion

Warm Up 1) A 2016 study from the State Department found that 46% of American citizens hold a passport. If repeated samples of 40 American citizens are.

Chapter 7 Sampling Distributions.

The mean value of land and buildings per acre for farms is $1300, with a standard deviation of $250. A random sample of size 36 is drawn. 1) What is the.

Chapter 7 Sampling Distributions.

From Samples to Populations

Quantitative Methods Varsha Varde.

Sampling Distributions

Chapter 7 Sampling Distributions.

Presentation transcript:

Statistical Reasoning for everyday life Intro to Probability and Statistics Mr. Spering – Room 113

8.1 Sampling Distributions NOTATION AND SYMBOL REVIEW: n… Sample size μ… Population mean σx… Population standard deviation Sx… Sample standard deviation SAMPLE MEAN

8.1 Sampling Distributions NOTATION AND SYMBOL REVIEW: z… Z-score (value compared with mean and σ) r… Correlation coefficient ∑x… Sum of x values P(x)… Probability of x

8.1 Sampling Distributions Sampling error… The error that is introduced when a sample is used to estimate a population. It does not include other sources of error, such as those due to biased sampling, bad survey questions, or recording mistakes. Would you expect the sampling error to increase or decrease if the sample size were increased? The sampling error is the observed differences in such things as means and standard deviations, or proportions, from the population from which the sample is taken. If error is truly random it should decrease with sample size. C.L.T If systematic the errors should not change regardless of sample.

8.1 Sampling Distributions Distribution of Sample Means… (Samples > 30) The larger the sample size, the more closely the sampling distribution approximates a normal distribution. In all cases, the mean of the sampling distribution equals the population mean. If only one sample is available, its sample mean, is the best estimate for the population mean. (C.L.T.) EXAMPLE: Texas has roughly 225,000 farms. The mean farm size is 582 acres. Suppose that for random samples of 100 farms, the distribution of sample means has a mean of 582 acres and a standard deviation of 15 acres. You select a random sample of 100 farms which have a mean size of 600. What is the probability of selecting another sample with a mean greater than 600 acres?

8.1 Sampling Distributions SAMPLE PROPORTIONS → PERCENTAGES & FRACTIONS More notations: Population proportions → Sample proportions → Distribution of sample proportions… The distribution of sample proportions results when we find the proportions in all possible samples of a given size. The larger the sample, the more closely the sampling distribution approximates a normal distribution. In all cases, the mean of the sampling distribution equals the population proportion. If only one sample is available it is the best estimate for the population proportion.

8.1 Sampling Distributions Class work: pg 343 # 1-15 all ?